An amusing discussion, eventually incorporating most of the important points. Save the Most Unusual circumstances, below a conservative(*) V1, STOP. Screw the brakes, just STOP. Above V1, you GO, execute MAX THRUST if necessary, fly the GA procedure and get that thing back on the ground. (Operations and maintenance will sort out the details,, later. In the instant, your ONLY responsibility is to return the airplane to terra firma and without hurting anyone.
The MTOW, distance and performance tables already include a modest fudge factor. Smart pilots double their fudge and never push the edge. They are still flying. Those who may have posed a bit too hard are dead. As is always the case, the Capt. is the ultimate judge and No Carrier will second-guess an AC who says, "No, I won't fly this leg" This is not about tanking some extra fuel - rarely questioned - but pushing the limits of the RWY and departure route. The smart girls and boys simply do not do it. Replacement crew? Smart ones ask why the priors declined and usually agree.
Even with three engines on a two engine airplane, you cannot fly it out of the sea, a lake, a river, or even a ditch! Smart pilots do not gamble.